exam2_sol_sp10 - Physics 101 Classical Physics Spring 2010...

Physics 101 Classical Physics Spring 2010
Exam 2 Solutions
Instructions : The answer sheets must be handed in as soon as time is called. You have until
10:20am.
Answer the following four multiple choice questions. Each question is worth 4 points.
1. A ball of mass 0.3 kg hits a wall and rebounds. Initially the magnitude of the
ball’s velocity is 7 m/s, but after rebound the magnitude of the velocity is 5
m/s. What is the impulse imparted to the ball by the wall?
(a) 1.8 kg m/s, (b) 2.1 kg m/s, (c) 3.6 kg m/s , (d) 0.6 kg m/s, (e) 1.5 kg m/s
The impulse is equal to the change in momentum, so
I = Δ ~ p = m ( ~ v
f
- ~ v
i
)
Defining the final velocity to be in the positive direction,
I = m (5 m/s - ( - 7 m/s)) = (0 . 3 kg)(12 m/s) = 3 . 6 kg · m/s
2. An object initially at rest breaks into two pieces as the result of an explosion.
One piece has twice the kinetic energy of the other piece. Which of the following
is the ratio of the masses of the two pieces?
(a) 1:1, (b) 2:1 , (c) 4:1, (d) 16:1, (e) more information is needed
Since the total momentum is conserved and initially zero, the velocities of the pieces must
be along the same axis with opposite signs. So, momentum conservation gives
m
1
v
1
= m
2
v
2
⇒ v
1
=
m
2
m
1
v
2
We are given that the kinetic energy of one of the pieces is twice that of the other.
2 T
1
= T
2
⇒ m
1
v
2
1
=
1
2
m
2
v
2
2
Plugging in the expression for v
1
above this becomes
m
1
m 2
2
m 2
1
v
2
2
=
1
2
m
2
v
2
2
m 2
2
m
1
=
1
2
m
2
m
2
m
1
=
1
2
So, the mass ratio is 2 : 1 .
1

3. A flywheel rotating with an initial angular velocity of 12 rev/s is brought to rest
in 6 s. If the angular acceleration is constant during this time, what is its value?
(a) -4 rad/s
2
, (b) -4 π rad/s 2 , (c) -2 rad/s 2 , (d) -1/ π rad/s 2 , (e) -72 rad/s 2
Since the angular acceleration is constant,
α =
Δ ω
Δ t
=
- 12 rev/s
6 s
2 π rad
1 rev
= - 4 π rad/s
2
4. The Earth wobbles—the axis about which it rotates each day actually rotates
its direction over time (this is a phenomenon called ‘precession’). While right
now it points toward the star Polaris (the North Star), in 13,000 years it circles
around and and will eventually point toward the star Vega in the opposite part
of the sky. 13,000 years after that, it will have circled all the way back and point
toward Polaris again. Which of the following statements is most likely to de-
scribe why this does or does not violate the conservation of angular momentum?
(a) The speed of rotation does not change, so the angular momentum is constant
and therefore conserved.
(b) Angular momentum does not have to be conserved, because the Earth is in
space, far away from anything else.
(c) The Earth is being acted on by an external torque from the gravity of
the Moon and the Sun, and so this changes the Earth’s angular momentum.
(d) Angular momentum is conserved, because the axis eventually gets back to
where it started so the net change is zero.